When it’s normal to have no idea what your returns are

The lingua franca of asset management regardless of strategy is returns. But this is not necessarily true in trading. In my own 21 years of trading, it was never even brought up internally. It gets mentioned somewhere far in the background. In vague terms at best. And even then, the context is more of a hurdle than a target.

We’re going to talk about this in 2 parts.

Today

I’ll walk through what this meant in the 3 phases of my career (with plenty of color interspersed):

  1. Being a market maker at SIG
  2. Running my own market-making group financed by a Chicago firm that backs traders
  3. As portfolio manager within a relative value volatility trading hedge fund. This last job was for an entity that was backed by LP money and therefore beholden to the concept, language, and delivery of returns. And yet, the idea of returns was alien to how I ran my business there.

Next week

I’ll connect this back to a reader question that got me thinking about all this in the first place:

How important is (il)liquidity in options when making risk-defined trades such as credit/debit spreads or buying single call/put options?

Hmm.

I can feel the doubt.

“Bruh, those lily pads are in different ponds, how we makin this leap?”

We gonna make it. Off we go…

At SIG

My first trading job for SIG where I had my own account and P/L was an equity options market maker on the AMEX floor.

The AMEX, like the NYSE, is a specialist system. There are “posts” where the options on a list of tickers trade. The specialist is like a lead market-maker who sees the full order book and is required to make a market according to a set of rules and guidelines. The specialist designation is a bundle of obligations and privileges. They must maintain an “orderly” market, set the vol curves which then disseminate electronic bids and offers for every strike and maturity for a name to the world. They are also entitled to 40% of the volume that trades on the bid or at the ask.

Market makers stand in front of the specialist post and announce any bids or offers that improve the specialists’ market. The market-makers are allowed to participate alongside the specialist on the bids and offers if they agree that they are “on the market”. My first year trading, I was a market-maker. The major names at my post were AIG, Qwest, Eastman Kodak, Corning, Cheesecake Factory, and about 25 other stocks. One that was notably missing because it was just delisted from that post — Enron.

As a novice trader, it was really about strapping on a helmet and getting experience. I wasn’t going to be taking massive risks but in the course of trading if I saw anything noteworthy I could discuss it with my manager to see if I should be. There were 3 notable things that happened in my time there.

  1. AIG accounting scandal (this was the only time I ever talked to Jeff Yass about a trade. UBS put up a giant print in the options and Jeff dm’d me to call him with details on one of the black phones placed near the trading posts. I was scared shitless to call because I didn’t do any part of the trade and was afraid he was going to undress me for missing it. He just listened, thanked me, and hung up. I never heard another word about it).
  2. Massive buyers of Qwest teeny puts by cap structure arb flow who were trading puts vs CDS. Selling them week after week in size and overhedging the hell out of them made my year. It was also stressful because up days were painful, but the stock leaked lower and the puts barely budged.

    [A year or two a colleague ran the same playbook in Xerox in much larger size and had an amazing year. If I remember correctly, that fellow was banned from Vegas casinos for card-counting by the time he was 22. He left SIG after that year, 25 or 26 years old, co-founded a prop firm and retired very wealthy in his 30s. Our wily friend also made the news for a buying a call option on a penthouse from its owner that ended up being the highest value residential RE trade in the city where it happened. Not a small city. One funny thing I remember about people’s impression of him — he was very lazy but insanely smart. And despite my personal belief that endurance and effort > brains, there were a lot of counterexamples to this back in those days. There were savants who struck it rich and peeled off. The billionaires in the options world were the savants who worked their asses off to build businesses, but the clever cats won life. You got $50mm in 2009 and your like 33 years old. You’re gonna triple it by age 50. In flip-flops with a flip phone.]

  3. I found a dividend in Kodak that was being priced in the wrong month. Which brings you to the question — how do you pick off the people who stand next to you all day with a structure that doesn’t tip them off too quickly and also disguises that it’s you?

    [This is a separate topic but trading cultures revere cleverness. It’s a game where the goal is to take people’s money. Any harmony is just a long-run game theoretic compromise. It is fundamentally adversarial. Can you see why effective altruism starts to look like effective autism when you consider the frames traders must adopt to deal with the discomfort of their decisions? At least back then the sociopaths were more forthcoming in their intentions rather than torturing normal people with trolley problems.]

After a year at that post, I was moved to one that included Microsoft (I was there when they announced their first dividend — it was special $3 div I believe), Oracle, and Expedia. That was 2003. After 2017, 2003 was my second least favorite year. There was less action compared to prior years and markets were getting tighter (the purely electronic ISE grabbed a ton of market share). I felt deeply discouraged. I came into the business near a peak and this was my first downcycle. I extrapolated doom.

So what were my returns in those first 2 years?

I have no idea. I had a close to $1mm profits in the first year and broke even in the second year.

I don’t know how much capital I used. In fact, they wouldn’t want me to know. For example, the margin I was paying financing charges on is likely much higher than it what it was in reality considering the difference in rates a small trader gets versus a giant client like SIG. It would only make sense for the partners to effectively lend me the difference rather than allowing me the credit for funding at the firm’s rates. It’s 6 in one hand, half dozen in the other when you zoom out but it does obscure your true rate of return. It wasn’t clear how much margin you are using or how much it varied. And they had no incentive to elucidate this.

If you were looking to leave then I’m sure you could have backed into a good guess for how much capital you needed. Which is critical if you are looking to build one of these businesses since of course it’s still a capital allocation decision whose ROI must be compared to other uses for the cash. But when you are making the donuts, there’s no talk of return.

So how do you talk about the business?

It’s raw dollars. Management figures “Ok, the average MSFT market maker for SIG should trade 5,000 lots a day for a penny of edge (remember the multiplier is 100, so it’s a true $1 per lot) times 252 trading days — the spot is worth $1.25mm per year”.

[If you make less, they’ll ding you in your bonus, if you make more, they say the trading was better that year so you were expected to make more — here’s your expected bonus. If you get discretionary bonuses you know the routine. You’ll get a verbal reach around in your bonus meeting, but then the number falls short of the rhetoric. I’ve been able to laugh about this for a long time now, but my wife can remember the days where my traders friends and I would plan what we would yell as we “flipped the desk over” 3 months in advance of our disappointing meetings. No matter how much you get paid, it’s always a letdown. She would joke about the Trader Wives Club where they’d have to hear us whine for 3 months before our reviews, and another week afterwards.]

In short, a trading spot occupied by a someone who knows what they’re doing has an expected p/l with a distribution. Based on the activity in the names that year, the value of the spot could be upgraded or downgraded for the following year. There’s always a dollar target and and the outcome is a debate about how much skill the trader brought to the result versus how the assumptions of volume, volatility, and competitive forces varied from the start-of-year forecast.

If the cost to man the spot makes sense compared to the expected p/l, someone will be assigned to it. Spots that are more valuable will be staffed with the more experienced/talented traders (ie you should expect that meme stocks are piloted by a prop firms’ top traders). So while there’s no concept of return, hurdles and opportunity costs are baked into the staffing decisions.


Backed by Prime

From 2008 until early 2012 I was backed by Prime International, a prop firm based in Chicago. Back then, they bankrolled about 100 traders, many in futures but there was several option pods of various sizes. I ran a mid-sized one and shared an office with their largest one (that pod was the largest market-maker in crude oil options in the late aughts).

These years were the most fun and learning I had in my career, outside the first year out of college as a trainee which was a zero-to-one combustion. I’ll save the stories for a non-print medium. I vaguely remember colleagues researching what it would take to create a small ice rink and get a penguin for the office. The fact that I would have put a 25 delta on it actually happening is a pretty good indication that this was not a normal work environment. Any job after this was gonna be a letdown but the floors’ days were numbered.

With the backer, everything was transparent. I was getting 70% of my p/l. I could see my daily margin. My shared and non-shared expenses. I could hire and fire as I wanted.

Yet again, no concept of return.

If you just looked at margin, you could back into an expectation that you should return 50-300% per year to make the gig worthwhile.

[This was in fact typical but I don’t think any pod back then was using more than $10mm and most utilizing less than $2mm. Floor trading isn’t that scalable. Ironically, the way to keep a floor well-fed is for fiduciaries to trade as if markets are more scalable than they actually are.]

Unfortunately margin isn’t a great denominator for returns. Buy a bunch of teeny options and you can mask risk. You could hunt for the cheapest thing to buy that makes a concern, defined too objectively on the back of assumptions, go away if you know what canned scenarios the risk group runs. I’m not saying this is done on a conscious or nefarious level but it’s too easy to affect the Ouija board by having a little extra preference for this strike or that maturity.

Computing return on average margin can also be weak depending on the nature of a strategy. Margin calculations are coarse proxies for risk. They aren’t custom enough for option traders. At one end they can be gamed, and on the other end they can be too conservative for arbitrage strategies (for example, no margin relief for WTI look-alike swaps if one leg is on ICE and the other on CME).

A picture is emerging. Return is difficult to compute because the denominator is murky.

We are accustomed to returns and volatilities. They let us use Sharpe ratios to measure risk-adjusted performance. But if we don’t have returns how do we get to risk limits that make sense? How do decide where to put capital?


Hedge fund days

In 2012, I moved to SF to build the commodity relative value volatility business for Parallax. It is a master fund with a host of sub strategies. LPs see returns but internally there’s no concept of returns at the strategy level. It’s just p/l that rolls up to the fund level. To be clear, this is typical for such a structure. It’s flexible.

The fund posts margin and manages risk such that the margin to equity ratio stays comfortably under 100% even in stressed conditions. Which means there’s always a cash buffer which can be held in T-bills, box spreads, or managed in any highly liquid way.

The sub-strategies margin requirements will bounce around based on the volatility and opportunities in the markets. Just to make up numbers, imagine the firm aum is $1B and runs 50% margin-to-equity. So in typical conditions, the margin requirement is $500mm.

Now consider that my margin requirement in the commodity book ranges between $20mm and $100mm depending on how much risk I’m taking. If I was a standalone fund and to be highly confident that my margin-to-equity wouldn’t exceed 80% than I’d need to raise $125mm. Most of the time I need much less, which causes a drag on returns but in the master fund structure I don’t really worry about this. The firm’s excess cash isn’t allocated to strategy as a hard constraint. The GP acts as the ultimate capital allocator internally.

So the best guess of what my returns are depend on the flawed denominator of average margin and relative to that number, they will always be worse if I’m a stand-alone fund because I need to raise far more capital than I’d typically be deploying.

How did it the business work in practice?

You’d come up with an annual expected p/l. In my case, the median was about 70% of the expectancy because I ran a positively skewed book.

[I was typically long vol convexity and often long gamma. When I was at Prime with my own money on the line, it was not uncommon to be paying 4 figure theta bills. I stood next to a guy that traded 100% of his own money that had a seven figure bill a few times a year. (Random thought but learned a lot about playing the player not the cards from him but this was a small market which he would turn into a game of heads-up no limit with the big customer. He recognized he had a lot of edge, and pushed. I hope he shifted gears when that was no longer the way you could play.)

In my fund book, you could buy a Porsche or Lambo every day with with the theta. That said — I kept a close eye on a very simple measure — don’t be long too much extrinsic premium unless there was a specific reason.

VRP language is something that feels like it comes from the asset management world not the floor trader world. There are exceptions. I knew some large short vol traders at every stop. The biggest lesson is that this game is far more artful than risk premia discourse pretends.

As for my own long vol bias and performance — this was not some trick of “Oh I lost half my years but won more in good years”. No backer, prop firm, or absolute return fund would tolerate that. I broke even or was down small 3 out of 20 years, made medium amounts most years and put up the numbers that drive the mean from the median around the GFC and the 3 year period spanning from the 2018 Volmageddon (although I wasn’t directly involved in that trade, it was the return of vol after the 2017 idiocy) through 2020. Look, the job pays when people are in pain. I don’t know what to tell you. The rest of the time I watch beta-maxxers and PE suits buy mansions. I write to feel prosocial. I don’t need trading to that feel that way. Sensing a dumb counterparty squirm, one who almost certainly was getting paid too much previously for charlatanism, is a reassuring hug from the god of markets as far as I’m concerned.

I am an agreeable human (I’m like 95th percentile on the Big Five personality test for this) but a highly disagreeable trader. Process, patience, fold, more patience, then f you sold. Boring, boring, boring, paper cuts, I hate this job, boring — violence. Put your style into simple words one day. It helps steer you back to the North Star whose light whose light you’ll most when your every decision feels like it takes you further into the dark.]

Back to the returns stuff. You peg an annual p/l target. Management implicitly considers how much risk needs to be tolerated to achieve that raw p/l, deems it satisfactory and off you go. Next year, the landscape is reviewed, growth initiatives weighed and you repeat a somewhat informal process. Any course-correction is mostly handled ad-hoc as the PM sees whether or not the environment calls for taking more or less risk. You can tell when there’s too many predators (entities who see the world in a similar way to us) vs prey (customers that have hedging or punting desires). There’s a time to hunt and time to hibernate. I say it all the time — this is a biological system not a Newtonian one.

So back to returns…it’s not quite right to think of return on margin. If you want to force a business like this into that framework you should probably just be conservative and consider how much AUM you’d need to run the strategy as a stand-alone fund. I’ll use a broad informed stroke. With a few hundred million in capital, I’d guess a strong manager with a trader mindset (as opposed to asset-manager mindset — if you’re in this business you know the difference so don’t @ me) could put up mean returns in the ballpark of 9-12% with the median between 50 and 70% of that.

[You can also see why many of these business are best housed within a fund that can flexibly allocate unutilized cash. The traders can be paid well enough to not tempt themselves into the brain damage of starting a fund of their own. To go out on your own has to be about more than money. There needs to a psychic reason to want your name on the door to endure what it takes to launch a fund.]

This is a damn good proposition because it behaves like long option position that you get paid to own. It’s unsurprising that the fees for the handful of managers who can do this (if you can even access them) are high. The proposition gets much worse if you’re taxable because it’s a short-term gain bonanza but of course many institutional allocators are tax-exempt.

Most of the risk lies in the ability for talented group of people to self-perpetuate themselves and the ability to assess that from the outside is probably almost zero. So all the usual caveats of active management apply.


Like I said earlier, next week I’ll tie this back to a seemingly unrelated question:

How important is (il)liquidity in options when making risk-defined trades such as credit/debit spreads or buying single call/put options?

Riffing on Paywalls, Trading & Options

Gather round. Let’s just chop it up in no particular order.

On Monday, I fired off an impromptu email with a trade I was doing. Disclaiming of course that it’s not a recommendation. I have no licenses and I’m not qualified to give financial advice. Buyer beware and all that. I sent it to paid subs only.

Actually, let me clarify the paywall. Last year I added some paid tiers on Substack. It was like $150/yr. There was also a $500 annual OG tier. For $150, it was just a chance to support the letter and OGs had that satisfaction plus a Zoom or IRL chat if they wanted. In other words, there was no extra content for paying. It was just a tip jar. I support other writers even if the content is free so I understand the impulse. Who am I to deny givers. So put the tiers in.

I have a friend in my book club who is a marketing ninja (people throw such superlatives around but this mf’er charges really high rates for good reason). He offered to “look at what I’m doing on the internet” pro bono. He saw how many people were supporting Moontower at the regular and especially OG level and remarked it was quite unusual for those percentages considering they weren’t getting any extra content. Paraphrasing: “Kris, people want to pay you. You just don’t give them an excuse. For many people it’s hard to pay for something even if they want to because the official price is zero. It’s a psychology thing.” Reminded me a bit of the “penny problem”.

I explained to him that I actually felt guilty or a sense of reciprocity for not delivering anything extra. But I feel strongly about giving away a lot for free. Charging also felt off.

Taking a longer, realistic view — time is time, and I give this letter a lot of time. I’m not some alien for whom this comes easy for. So the eggshell that idealism always rests in has cracks in the form of opportunity cost. The compromise to satisfy both my guilt and test his thesis that more people wanted to pay was to paywall a small fraction of my writing.

Anyway, that’s the genesis of the paywall. I’m happy with the mix. I feel better about all the guilts — opportunity cost of time, giving extra to payers, and not withholding what I hope is value for people who won’t or can’t pay.

The paywall also seemed like the right venue for sharing a trade I was doing. It’s a bit safer space since I don’t think anyone pays to hate-follow.

I’ll add— if you converted to paying because you think I discuss trades all-the-time you’ll be disappointed. I suspect I might do it more especially as my personal trading infra gets better with moontower.ai but I’d rather underpromise on the writing and let this place be a source of pleasant surprise instead of having it start from a transactional place where I feel the invisible pressure of coming up with stuff for the sake of delivering something that sounds useful. If I tell you I like something it’s because I do it. And it might be dumb. But that’s why it’s never a recommendation. You can only count on me translating what the turd-throwing monkey in my brain says back to you. You decide if that’s worth paying for, either way I’m publishing plenty of free stuff and some not free.

Moving on.

I did in fact do a trade. If you follow me on Twitter, I’m transparent and I even shared screenshots. I’m more Whimpering Puppy than Roaring Kitty but my real-time thought narration is less cryptic than memes. SO, I have that going for me.

I bought the GME June 20/30 call spread unhedged. I only bought 20. My intention was to buy 100. I was comfortable risking about $25k. I got filled at $2.08 giving me almost 4-1 if the stock expires $30 or higher. Unfortunately I left a bunch of dead soldiers (unfilled orders) behind and the stock got up to $30 the same day. $4k turned into $8k and I’m just mad. As Agustin Lebron preaches in Laws of Trading — “you are never happy with the size you trade”. It’s always too much too little in hindsight.

Although I didn’t share the trade idea in the free substack, I did share lots of thoughts publicly:

Messing around a bit. Used an option calculator and ran 300% flat vol sheets vs skewed vol sheets that roughly fit the market just to see how different the distributions are (stock ref $25 in $GME)

Which was a follow-up to:

Flat vol is what old people would call flat sheets. As if you ran the same vol on every strike. My gut market on this call spread if I’m allowed to be wide would have been $7.75-$8.75 knowing it was volatile squeeze stock with 2 weeks to expiry.

[This isn’t actually a short squeeze but it’s the only mental model I can match it to]

Looking at the table, my $7.75 bid would simply get tattoo’d. Anyway, hoping tomorrow the setup invites a little gamble. If we get more of the same flow as today, I’ll get the chance.

Back to the butterflies:

Fly density is just butterfly centered on the middle strike divided by the strike width. This is why vertical spreads are model free bets on the distribution. A lot of call skew or vol pushes the modal outcome to the left.

High call skew makes call spreads cheaper which implies lower probabilities of the stock going up. Which is why my original tweet is looking at how cheap the call spreads are and the market implying the stock lower.

Here’s one more this time including what a regular 30% stock distribution looks like to the picture (again using flat vols):

Image

You are getting unusually high odds to bet the stock is not going down by June expiration.

This is the same idea I’ve pointed out in winter gas or H/J nat gas CSO’s. When call skew is nuclear or stocks short squeeze for options market bidding for upside actually implies the stock is probably going to drop (which is consensus in a squeeze…it’s just a matter of when and how fast).

The down moves are stabilizing. Think of the up move as potential energy of a stretched rubber band. No matter how far you pull it the expected snap back point is the same. In fact, the bigger the squeeze the more likely the capitulation happens because the last short says uncle and represents the last buyer. There’s nobody left to buy.

This is why when when assets squeeze the put spreads get expensive. Consensus is down not up. Up is destabilizing, higher vol territory. Remember how you want to own the options AWAY from where it expires.

This is a classic demonstration. The market wants the options in the direction of the skew. It wants the “it probably won’t get there but if it does things are gonna break, yee haw!” It doesn’t want the options of where the stock will land. Or inverting, where the options are cheap (the cheapest body of a fly, therefore the most expensive butterfly) is where the stock is implied to land.

This account had good questions. I gave my best answers.

One account rebutted that options don’t just sit overnight with positive EV sitting in them.

Hey, I mostly agree. But this is a coin flip I believe the odds compensate for. Nobody knows where it’s landing. If RK rolls or changes his position the odds change…the most egregious dislocations in the surface probably fair up and something else breaks. In the tree of possibilities, the trade can work simply by the turn card coming out (ie new information in the form of flow that shuffles the deck in a new way). I don’t need to take this into expiry. I think there’s edge in the levels.

Here’s the thing — nobody has some quant model that knows where this thing is landing. This is a pure trading situation. Of course, I can be wrong. Hell, I told my wife I’d guess I have a 50% chance of incinerating the premium which is much higher than what flat sheets or a lower vol name would suggest.

But I have several ways to win. If go to the grave with these, I do think I’m getting odds because the market had to absorb this flow by moving the spread. It can’t diversify it away. Another way to win or at least manage the position comes from trusting my judgement on how to think about the matrix. You do this long enough, you chunk an options board the way a chess player chunks familiar patterns. “Hmm, that fly looks too cheap compared to that one…ahh when I try to execute I find out it’s not really there”.

As trading goes, this is not the hard part. What’s hard is when things are grinding tick by tick. That’s a miserable nerd market that burns my eyes. I don’t have opinions on stuff where everyone can think all day and night about what something is worth. In fact I don’t have opinions often. Right back to the “options don’t just have positive EV sitting in them”.

I do think you can make better decisions in the options landscape but that not the same bar as being a pure alpha option trader. That last bar is really high. The market likes to give you false directions to that party. It’s important to know what circumstances your heuristics are more likely to apply. Trading requires the tacit knowledge of when to switch gears between “I need to act without full info but right now I can act with even less info because the amount of info anyone has is not as high as it usually is”.


One last bit.

The reason I even looked at GME closely was serendipity. A friend had an angle on GME he wanted to bounce off me. It was a pet idea. Kind of weird but also something I thought similarly about in the psychology (which I don’t think is a view most people managing money would come to). It’s not a 4D chess thing either which is something I’m generally skeptical of anyway.

But chatting yesterday, he made an off-hand comment that highlighted why options are so interesting.

He texted:

all the probabilities are skewed to make people get long lol

This is exactly, what the cheap call spreads do. Which is why we say “they imply the stock much lower”. Again look at those fly distribution pics. You only make that statement if you understand options. But here’s the rub…what is the counterforce? What’s the thing that makes people want to get short not long?

The stock price itself.

It says get short. If you have an investor’s horizon you think, why is anyone paying $9B for a couple billions worth of T-bills*? Meanwhile, the options offer odds to get long.

[*On Wednesday it came out that the at-the-money share offering raised $2B….hmm and all it took was a few days of the stock trading in the 20s to absorb it…sounds bullish to me.]

The question of fundamental value has zero relevance to the now. It’s like using a yardstick to take the temperature. Don’t mix up the dashboards you use for long-term ideas for the gauges you use to consider the short-term.


And finally, we couldn’t resist…

while we are about to double our ETF coverage on moontower.ai we just had to add GME.

Image

Seriously, I’m stoked about how moontower.ai is coming along.

(If you use options, you should check it out. If you are just curious you can still sign up for free for the educational materials and MoontowerGPT)

A collateral benefit of the moontower.ai work is personally getting to spend more time in Jupyter notebooks as I sandbox ideas that are coming down the pipe. Coding is not a personal strength, I rely on Copilot A LOT. I only recently started using Git. But getting to build, learn, write, code, and bring together analytics in a way that leads to better decisions, practical actions, and teach is a super satisfying way to spend time. [By the way, nothing I code goes into production, that would be malpractice.]

These opportunities wouldn’t have come together if you didn’t give me a little hamster wheel in your brain to run on. I know if I do a good job on all fronts that elusive sweet spot of “sustainable because it’s valuable” and satisfying is possible.

So thank you.

Stay Groovy

a birdie asked how to model a 1-day option

It’s going to shock you to hear it, but I get emailed a lot of option questions. I’ve gotten some that are pages long with commentary, prices, blood type.

This is one of the reasons I put the shingle up for calls. I’m definitely not reading all that free, but also I can talk through options stuff way faster than I can read and write about it. You’ll say 500 words about what your doing and I’ll collapse it into floor trader grunts in the time it takes to pick up a handset and say “sold”.

I spent my whole adult life having to make option decisions in a few seconds. This is not anything special — talk with any market-maker and their fluency with calls and puts seems like a parlor trick. Options are just another language and being fluent in it means you think in that language natively. The old floor folk can even sign in options as fast as you can talk. (I can read the signing but I was the tail end of futures being traded in the pit and not on Globex. I never developed a large hand signal vocabulary).

That said, if a sub sends me a question that I can peck on my phone in a few minutes I’ll just answer it. (Also I read every email I get and try to respond to all of them even if it’s to acknowledge that both I and the sender are humans worthy of not being ignored.)

If responding to an email takes more than a few minutes I’ll pass it through the “would other people care about the answer to this question?” filter. If so, I can kill 2 birds with one stone. Oh my god, F me that’s a horrid idiom. The first person who ever said that should have been locked up on the spot cause that’s I-knew-he-was-a-serial-killer-when-he-was-nine level of clue. I never thought about the literal meaning of that expression until I typed it.

Re-phrasing — today is one of those moontowers where I can pick up the 7-10 split by sharing a response to a reader question that you might find useful.

Reader question:

Do you know of any way to model an option’s price intraday?

My response:

2 things I’d think about:

1. Intraday I would think in terms of straddle prices and price changes and compare that to tick vols (but the tick vols themselves can also be in price space not vol space)

2. Modelling the fraction of a day’s variance that typically accumulates every hour (for example the open represent more of the days volatility then any random 15 minute interval)

Reader reply:

When you say you would think in terms of straddle prices and price changes, how would that be used to model the price of a specific option? For example, if someone wanted to model the price of the 190 strike call 5/24 by the hour tomorrow relative to AAPL’s price, what should they do to get a rough idea? 

 

I’d start with the question of:

“What do you think the straddle is worth every hour?”

straddle represents the mean absolute deviation (MAD) which is 80% of the volatility or standard deviation of return.

If you think AAPL moves 1% per day then the straddle is worth 1% at the start of the day. If strike is ATM then the call is worth 50 bps.

The value of the straddle changes by root time (assuming vol is unchanged).

[See Visual Derivation Of The Straddle Approximation]

So if half the day is gone, the straddle is worth: 1% * sqrt(.5) = .71%

The question is at what time do you think only 1/2 the day’s volatility remains?

This question applies to every hour of the day.

The entire concept of “intraday decay curves” is area of active inquiry for any market-maker so I don’t have an answer key but the problem is familiar.

In practice, I’ve tackled this with a blend of lazy guessing and leaning on some quant research.

The lazy way

The 80/20 solution or guess would be to assume volatility transpires at the same rate volume unfolds over the course of the day.

I prompted perplexity.ai with “vwap volume distribution over the day”. To my delight it didn’t send me down the circus internet, but actually said something smart:

The volume-weighted average price (VWAP) is calculated by dividing the total dollar amount traded for a security over a specific time period by the total volume traded during that same period. This means that prices at which larger volumes were traded have a greater impact on the VWAP calculation than prices with smaller volumes.

To calculate VWAP accurately, it is important to consider the volume distribution over the trading day. Historically, volume is not evenly distributed throughout the day – there are typically periods of higher and lower trading activity.

Many trading algorithms account for this by using historical volume profiles to predict the expected volume distribution over the upcoming trading day. The algorithm then slices the total order into smaller “child orders” that are released at predetermined times based on the forecasted volume distribution.

For example, if 17% of the day’s total volume historically trades in the first hour, the algorithm would aim to execute 17% of the total order during that first hour period.

Get your hands on historical volume profiles and you have a solid start. VWAP algos are commoditized and rest on that research so it shouldn’t be hard to track down.

The quant way

You can use tick data to compute realized variance for each hour and divide by the sum of all the variances for the day to see the proportion by interval. You can use many days data as well as many names to get a cross-sectional perspective.

You will need to treat the period from the prior close to the open in some coherent manner as well. Like you could take the point-to-point variance from the previous close to open divided by the close to close variance over many samples and names and then you can make a statement like “25% of the variance happens overnight.”

That means the remaining hourly variances are then divided by a variance of only .75 of the expected daily variance. Over many days of doing this you will likely get a strong sense of when on average half a day’s variance has transpired.


Extra thoughts

 

  1. Computing tick vols is a quant rabbit hole of its own. When you come across the words “bid-ask bounce” and “volatility signature plot” you are reading the right stuff.
  2. I’m not a quant researcher. I’m a hacker. I throw numbers in spreadsheets or if I’m really ambitious Python, and turn the crank until I see the shape of the problem. So my methodology above is a zoomed out answer but once you make contact with data the specific details will not go smoothly. Nature of the beast. But the approach is directionally correct you just have to savor the data-wrangling gruel. For example, how many data points are enough? I don’t know — keep adding more until the variations in proportions seem to stabilize at some quantity.

    An instinct one develops with enough practice is to know whether your cobbled-together “tape and twine” analysis has a rigor that is proportional to required precision of your use-case. If whatever I’m doing is going to break because I don’t truly understand what “degrees of freedom” means then I just need enough taste to know that I should get a quant’s help.

    Discerning how rigorous you need to be is part of being an efficient resource allocator. How much time do you spend on pricing vs execution vs figuring out how to hedge less vs exploring names like not AAPL or other high volume names where Citadel & SIG’s market-makers are trading from the cockpit of F-22s?

What Equity Option Traders Can Learn From Commodity Options

GME share price started the month around $11. On Friday May 10th, it closed $17.46. Monday it was about 80% to $31. Tuesday it climbed >50% closing at $48.75 before it would give back over half its gains just as quickly.

In a twitter thread @DeepDishEnjoyer, a former market-maker, called attention to what happened with the July expiry $10 strike put — despite a huge rally the put went up in value. Obviously implied volatility exploded.

Let’s follow along in the thread:

This is quite odd from a first principles perspective. GME closed 17 handle on Friday. Today it meme squeezed up because of Roaring Kitty. A basic model is: it continues meme’ing – then these puts expire worthless or the meme ends and we go back to where we were at at Friday. But note that you could have sold these puts at 75 cents today even though they closed in the 50s on Friday!!!! They should be actually be worth *less* since there is no state of the world where downside vol increased.

He continues:

That’s easily anywhere from 20-40 cents of EV on these puts. And indeed that’s where these puts landed now. So why does it happen? Well, market makers don’t pay a large amount of attention to the wings of their vol surface. ATM implied vol got correctly bid, but they moved the…rest of the surface in parallel EVEN THOUGH THAT MAKES NO SENSE IN A SCENARIO WHERE A STOCK MEME GAPPED UP. Again, vol follows fairly two discrete paths that are intimately tied to stock price – vol is high when the stock is memeing, vol necessarily dies down when it stops.

At the money implied vol should increase. But the strike vol of the 10 strike put should not be massively increasing as the probability of going *below* 10 has not increased today from yesterday, while the options market is implying it has.

So did the IV on those puts go up “too much”?

Settle in. Lots to discuss.

I used the price chart of the put to price the options with a Black Scholes European-style calculator (the American/European thing isn’t important for this).

We start with May 10th just to establish the first elevated IV before stepping through the insanity of the May 13th morning.

It’s a bit hand-wavey since I didn’t know where the spot price was with every corresponding put price on that Monday morning. I assume the put price surged and eased while the spot price remains at $31. The illustration will be valid even if the exact numbers aren’t.

The put price on May 13

For the next section, keep in mind that N(d2) represents probability of option expiring in-the-money.

Stepping through the option prices…

@DeepDishEnjoyer said at $.75 the put implied an even higher chance of going in the money with the stock at $31 than it did when the stock was $17.50.

That checks out in the option model.

It also reflects experienced intuition by DeepDishEnjoyer because I doubt he manually computed N(d2).

The option beginner could have exclaimed “the implied probability isn’t higher — the delta of the put went from .08 to .04!” If you’ve been at the moontower for awhile you understand in high volatility names delta does not equal probability (if you are a new reader then I point you to a top-5 most read post: Lessons From The .50 Delta Option).

When the vol eases back to 175%, still higher than the previous day but off the high, the put’s probability falls to 14% (and the delta falls meagerly from .04 to .03).

Our twitter friend used a sense of implied probability to conclude that the put price expanded too much. And because he says:

there’s easily anywhere from 20-40 cents of EV on these puts. And indeed that’s where these puts landed now

I can infer that while he thought the $.75 price was too high, he may not have a strong opinion on the $.40 price. A price that still represents a much higher IV (175%) vs Friday (112%).

Smacks of a lot of experience. It was also a slightly different way than I would have thought about it.

How my instincts work in such situations

My reflex is also to think in terms of probability. However, I don’t reach for an N(d2) calculator.

I look at put spreads. Tradeable odds.

When DeepDishEnjoyer says the $.75 price is too high a probability, he’s collapsing a lot of compiled mental code into a comment. It’s worth unwrapping.

The price of an option reflects the probability of going in the money as well as how far ITM it can go. The divergence of the delta and N(d2) is model-based clue — since the maximum payoff on that put is capped at $10 then the exploding IV is mostly operating on the probability portion.

My native instinct when thinking about probability is to look at the put spreads since verticals are model-free over/under style bets.

See:

When I think “The $10 put is too high” I hear 2 possibilities:

a) The volatility is too high

or

b) There is a slab of put spreads on the surface that are too cheap where you should buy a higher strike put and sell the expensive $10 put. In this case, you believe the probability of finishing in the money for the $10 put is too high, but the implied probability of the stock going back to $10 is too low.

In other words, we get option trades ideas that are in opposition!

  • If you believe volatility is too high you should consider selling at-the-money options which have more vega and at least locally less exposure to high-order moments. (Since the market is volatile, you might sell straddles, see the stock move, and your options become OTM, leaving you exposed to those higher-order moments anyway.)
  • If you think the $10 put is too high, and buy a put spread because you think the implied probability of going to $10 is underpriced. But this is a long vol position.

This is the $20 put if you priced it at 206% vol as well.

Notice how the probability of going ITM is 49% despite the strike being 33% out-of-the-money. Again, even though the probability looks high at nearly 50%, the delta is only .17

So how do we parse this?

We agree the $10 put is too high at $.75…do we sell it as the short leg of a put spread offering 1.8 to 1 on the meme situation ending by mid-July?

The price action looks like that $.75 print was fleeting and likely hard to get on. I doubt the market-makers mispriced it so much as recognized that buyers on a Monday morning could be sloppy traders thinking “I’m buying puts because this stock action is dumb” and were directionally aware but not vol aware. Rip the surface up, print the customers, take it back down to a spot that balances a more level-headed meeting price of buyers and sellers.

It’s hard to disagree with DeepDishEnjoyer. The puts were an outright sale. Probably hard to execute in the fleeting window but the point stands.

The way this situation unfolded, the speed of the rally, occurrence over a weekend, and retrace within a few days reminds me of early 2021 when SLV got aped from about $24 to $27 for a hot second.

The vols blew out across the surface (especially the calls) and I had exactly the same response as DeepDishEnjoyer — sell the downside puts.

Unfortunately…

SLV did a great job pricing them. The best you could get on the 27/24 put spread was an even money payout on the stock retracing back to 24. Any “normal” surface would give you pretty nice odds of a stock falling 10% but the surface was telling you that a 10% sell-off was “home”.

The put vols way underperformed the ATM and call vols. The market understood that those puts were trash and didn’t bid them up. Which made the put spreads, the structure you want to buy, a well-priced risk/reward. Nothing to see here.

The up move in SLV was not as extreme as GME. The vol expansion was only a doubling from about 35 to 70. So those OTM puts weren’t suddenly more expensive than they were pre-move. They just weren’t down as much as you’d expect.

If the stock went back down you would have lost on an unhedged basis. If were hedged then you risk the stock rallying further. And then if you did hedge and the stock fell what delta would you want to be short on? The p/l from a well-priced option trade is just path noise with no compensation.

Here’s a scenario any experienced option trader will relate to:

The stock sells off moderately, the vol comes in, which pushes that strike further OTM and the strike vol rolls up the skew curve as the option goes from say 20 delta to 5 delta despite becoming closer in moneyness. You’ll win on this move, but not as much as you’d like, and if you decide to cover the teeny put when you cover your stock shares you’ll pay a small exit tax on the way out. None of this will have felt worth the brain damage because the option market got it right from the start.

[There was a fleeting moment of edge in all this — there was a window of call buying at over 110% after the open that later settled in to being 90% IV for the next few days. If you missed that window, sure you could have sold 90% vol and thought that was high but you’re basically trading at fair value because there was liquid flow at both sides of that level.

Note the similarity to the GME puts. A fleeting window in the am before options settle into fair. The lesson — only trade a fast market on the open if you want to be a hero and willing to risk being a donkey. Unfortunately, getting filled is not a good sign. If you’d prefer a “fairer” execution you should wait.]

Commodity markets as teachers

I went for a hike during that SLV week with friend who runs a commodity vol fund. We had this moment:

I restored in HD 4k the original "Spider-Man Pointing at ...
“You wanted to buy put spreads and passed too?!”

We had the same instincts. And the same conclusion. Sell the puts, doh, they don’t look expensive compared to the rest of the surface, dammit, I hate this place.

We joked about how anyone who has ever traded nat gas has these same instincts. It can be April, gas futures for the upcoming Winter could be $8 and no matter which put spread you try to buy to bet gas goes right back to $3 by expiry pays no more than 3-to-1. If you have no frame of reference for odds…imagine being paid only 3-to-1 on a 63% selloff.

I’m looking at Jan25 options in ARKK right now. The 23/17 put spread costs about $.20 with the stock at $45. This spread can be worth $6. You’re getting 29-to-1 on a 63% selloff.

The other joke we made is that in commodities you find these regimes where wingy options just don’t change in price unless insanity happens. Your model says the option has a 5d but the experience is they behave on a 0 delta. This sound ridiculous until you watch people blow out because they have this wrong (nat gas is full of stories of people getting rinsed owning puts on massive selloffs including a large mm).

As a trader, when you see a crazy situation like a meme-stock, it’s useful to ask yourself — what market regularly has this behavior? Is it a market with lots of volume, a centralized/transparent order book, and 20+ years of institutionalized tacit knowledge of how to price options on such weirdness? Nat gas says “check, check and check”.

When a meme stock squeezes, does JANE SIGCIT just yell turn off “equity sheets run gas skew in GME?”

It’s not total overlap but a squeeze is balancing the same forces I explain in What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s Gold:

The truth is the gas market is very smart. The options are priced in such a way that the path is highly respected. The OTM calls are jacked, because if we see H gas trade $10, the straddle will go nuclear.

Why? Because it has to balance 2 opposing forces.

  1. It’s not clear how high the price can go in a true squeeze or shortage
  2. The MOST likely scenario is the price collapses back to $3 or $4.

Let me repeat how gnarly this is.

The price has an unbounded upside, but it will most likely end up in the $3-$4 range.

Try to think of a strategy to trade that.

Good luck.

  • Wanna trade verticals? You will find they all point right back to the $3 to $4 range.
  • Upside butterflies which are the spread of call spreads (that’s not a typo…that’s what a fly is…a spread of spreads. Prove it to yourself with a pencil and paper) are zeros.

As a matter of prospecting, you can expect that each time a market starts “meme’ing” the playbooks become more obvious for the surface setters. That said, market-makers are exceptional pattern-matchers so if you have a reason why a familiar setup will have a different endpoint, you’ll be able to find great prices. But if you have the consensus “this thing is headed back home” view know that the prices already reflect that. You’re just tossing coins for even money.

GME was Groundhog’s Day. This is from the 2021 post How Options Confuse Directional Traders:

SLV downside

We’re going to come back to silver again in a moment.

In all this writing, I hope the message is coming across — you should not touch options if you have a directional opinion but not a vol opinion.

On Monday, we held the moontower.ai community zoom. We talked about the newly released Moontower Mission Plan series. The core goal of the series is to walk a user through the process of developing a volatility opinion (or “axe” as in “axe to grind” — trading lingo).

As we walked through the steps, I found that SLV near-dated downside (ie 1 month) looked like a sale.

The IV was elevated and the term structure strongly descending so we proposed selling near-dated…

…but then we check the VRP (volatility risk premium) to see how the IV looked compared to recent realized vol and found a healthy amount of carry.

So we like selling near-dated SLV vol.

Now SLV has been rallying along with GLD. This thread by @SantiagoAuFund makes the case for a tactical short directional position in silver. The sentiment and COT positioning reasons are the ones that resonate most with me.

[Plus the fact that he’s being attacked for being bearish. I like when a trade offends people — if everyone is bulled up then the market is more likely to compensate the sellers since that’s whose service is needed. And if positioning indicates that speculators are already very long, then that’s embedded in the current price plus there’s less people left to buy. I hold no long term view on silver — I just like the tactical idea.]

Santiago expressed his bet via buying puts. This is where we differ. SLV vol looks like a sale so I want to express the bearish directional view in a short vol way. I also prefer simplicity. So I’d limit the trade expressions to:

  1. Selling ATM or ITM callsThe skew in the one month 25d puts according to our metrics is in the 47th percentile so it’s pretty fair therefore I don’t feel ripped off selling the ITM calls. (You could also sell the OTM puts and short the stock on a 1-1 ratio. It’s synthetically the same trade.)
  2. Sell straddles where the call is ITM.Same trade as the earlier one, but the initial delta is not as short (so if your directional conviction isn’t strong. Also if you sold OTM puts and hedge with half the number of shares this is synthetically an ITM straddle. The shares turn 1/2 the puts into synthetic calls. So if you sold 10 OTM puts and 500 shares your synthetically short 5 ITM straddles. Put-call parity is fun.)
  3. You could sell the calls and cap your risk by buying an OTM call.This is a short call spread. Since you are buying a higher strike call, your initial vega will not be as short. The wider the call spread the more the risk looks like a naked short call and the more short vol you are expressing (not to mention shorter deltas).
  4. A more advanced trade could be to buy 1×2 put spreadsYou could buy an ITM put to sell 2 OTM puts. You can find the strikes that dial in the desired initial delta and vega. But you can also see that this is the equivalent of buying a put spread and selling an extra OTM put. Or selling a straddle and buying a single OTM option to hedge. Options are Legos to build the structures you want, but just as a chess player chunks positions into familiar patterns, options can all be reduced to a combination of straddles and verticals (if we stick to a single expiry).

Ok, that’s enough for today.

Also, disclaim disclaim disclaim. You own your own decisions. I’m just saying what I see not recommending you do anything.

Weighting An Options Pair Trade

An option trader pinged me about a trade between a correlated pair of names whose IV ratio was trading at an extreme level compared to the ratio of realized volatilities that the pair has experienced in the past.

This trader is experienced. He understood that pitting vanilla options against one another invites path dependence. It’s worth spelling that out with a demonstration:

Imagine both assets are trading for $100 so you buy the 100 strike straddle in asset A and short the 100 strike straddle in asset B. Once these assets start bouncing around the moneyness of the straddle positions will get out of sync. After a week if both assets realize the same volatility but the path of A means it’s up 5% and the path of B means its up only 2% then you will have more gamma and theta in B because the straddle is closer to at-the-money (ATM). The further you get from a strike the more your exposure “goes away”. Far OTM options spit off smaller greeks and are less sensitive to changes in underlying price or volatility.

Let’s get to the question.

He was theta-weighting the trade instead of vega-weighting the trade. He wanted to know if I would do the same.

I’ll give examples of how each approach will end up weighting the legs, how I’d weight the trade, how to map weightings to the nature of a relationship, and even what greeks depend on.

By the time you finish this post, you will be able to understand the risks of different weightings and how to compute weightings in your head knowing nothing else except spot prices and ATM vols.

Let’s start with definitions.

Delta

Change in option price for a $1 change in the stock price

If an option has a .50 delta and the stock increases by $1, the option value increases by $.50

If it was a put option the delta would be negative. If the option has a -.50 delta and the stock increases by $1, the option falls by $.50. If the stock had fallen by $1 then the option increases in value by $.50

Vega

Change in option price for a 1 point change in the implied volatility

If an option has .20 of vega than a 1 point increase in implied vol, for example from 15% to 16%, the value of the option increases by $.20

If implied volatility fell from 15% to 14%, the option loses $.20

Gamma

The change in the delta for a $1 change in the stock price

If an option has .05 gamma and .50 delta and the option goes $1 more in-the-money then the option delta increases from .50 to .55. The option is becoming more sensitive to the stock price. As an option goes far in-the-money its delta continues to increase because of gamma until it approaches 1.00. At that point the option is so far in-the-money it moves 1-to-1 with the stock price.

If our .50 delta option with .05 gamma falls $1 out-of-the money its delta falls to .45. It becomes less sensitive to the stock price on the subsequent move. If the option continues to fall further out-of-the-money, its delta will fall to zero and changes in the stock price will have no impact on the option value. It is so far out-of-the-money it’s likely worthless.

Theta

The amount an option price decays when 1 day elapses

A key observation which harkens back to the path-dependance demonstration:

Greeks, ie option sensitivities, are a single snapshot in time.

They change if any of the inputs change — volatility, time to expiry, interest rates/divs, or moneyness (ie the distance of the stock price from the strike price).

This is important because when we place a pair trade (long one option and short another on different names) we initialize it by trying to do it in a vega or theta neutral way. We aren’t trying to make a statement about the general implied vol, but the relationship of the implied vols to one another.

Getting back to the reader’s question…do we initialize neutrality with vega or theta?

The answer depends on what you are trying to capture when you bet on the relationship of the implied vols.

What is it about the relationship that you are trying to make a statement about?

  • Do you believe the implied vols should trade at a certain spread to each other?

    For example, stock A’s implied volatility is typically 5 points higher than stock B, but they are both trading for the same volatility so you want to buy a straddle on A and short a straddle on B. How do you weight that trade?

  • Do you believe the implied vols should trade at a certain ratio to each other?

    For example, you believe stock A should trade at a 50% higher volatility then stock B. If both are trading for 10% volatility, you want to buy straddles on A and short straddles on B. How do you size those trades?

There can be a world of difference between a spread vs ratio relationship.

If stock A is 20% volatility and stock B is 10% volatility the ratio is 2 and spread is 10 points.

If both volatilities double then the ratio is constant but the spread is now 20 points!

If you weighted the trade to bet on the ratio your p/l is 0. If you weighted the trade assuming the spread would stay fixed, your pair trade is now spitting off a bunch of p/l.

The easiest way to build intuition for this is a toy example.

Consider 2 stocks, HighVol and LowVol. They are both $100 and we are going to initiate a pair trade in a 6-month options.

I used an option calculator to compute the greeks for the 2 names:

Observations

  1. Regardless of the volatility, the options on each name have the same vega.
  2. HighVol options, which are twice the volatility of LowVol, have twice the theta and half the gamma.

    Intuition:

    theta: An option that has 2x the volatility, all else equal, is worth 2x the premium of the lower vol option. It has 2x the amount of theta to decay to zero.

    gamma: A $1 move is twice as significant to LowVol than HighVol. Just like a 1% move in SPY is more meaningful than a 1% move in TSLA.

    Higher implied vols mean bigger thetas and smaller gammas


P/L under both weighting schemes if volatility doubles

Vega-weighting

If you vega-weight the pair trade you will trade the same amount of options in each name. Why?

If you short 100 contracts of HighVol your net vega will be -2810.

-100 x .281 x 100 share multiplier

If you buy 100 contracts of LowVol your net vega will be +2820

+100 x .282 x 100 share multiplier

Net vega = -2810 + 2820 = 10 which rounds to zero. If the vol in both names goes up by 1 point you make $10 which is 1/10 of a penny on 100 option contracts. Less than the commission. Mark it zero.

We’ll just round the vega positions to long and short 2800 for the 2 legs of the trade.

What happens when vol doubles?

Notice that vega per option doesn’t really change. Computing the p/l is straight forward.

Your long option position in LowVol increased by 15 vol points (15% to 30%).

P/L on long options = 15 points x 2800 = $42,000

P/L on short options = 30 points x -2800 = -$84,000

Total p/l for pairs trade = -$42,000

If you vega-weight a trade, you are exposed to the spread! The ratio stayed the same but you experienced p/l. This weighting was not a bet on the ratio!

 

Theta-weighting

Let’s buy LowVol and short HighVol again but this time weight the legs by theta. Remember, LowVol has half the theta as HighVol so to be theta-neutral we must buy 2x as many options in LowVol.

Let’s buy 200 options in LowVol vs shorting 100 option in HighVol.

We are theta-neutral, but what’s our net vega?

Vega in LowVol = 200 contracts x .28 x 100 multiplier = 5,600 vega

Vega in HighVol = 100 contracts x -.28 x 100 multiplier = -2,800 vega

Net vega = +2,800

A theta-neutral weighting means we are long vol.

Once again let’s shock the vol but keep the ratio constant.

If LowVol goes from 15% to 30% we make 15 vol points x 5,600 = $84,000

This perfectly offsets the $84,000 loss we’ll experience when we ride a short 2,800 vega position in HighVol up 30 points as vol doubles form 30% to 60%.

Theta weighting neutralizes our position to the ratio, but it is exposed to the spread!

 

Consolidating what we know

If we balance thetas:

  • our positions will have a net vega
  • we are hedged against the ratio of the vols but not the spread

If we balance vegas:

  • our positions will have a net theta
  • we are hedged against the spread but not the ratio of the vols

 

How would I weight an option pair trade?

I generally look at trades as ratios. Why?

Because they are not level-dependent.

If the absolute level of vol is in a tight range then the spread will be stable. For example if you trade WTI crude options against Brent crude the vols are similar. If you buy 5,000 vega in WTI at 29 vol and hedge by shorting 5,000 vega in Brent at 30 vol you are vega-weighting the pair. And that will suffice for small changes in volatility. The ratio will move around a bit, but for the most part the vol spread will be pretty fixed and you’re roughly hedged so long as that’s true.

But over wide changes in volatility, the ratio is more likely to hold. If there are 2 names that are 10% and 20% vol respectively and vol roofs, I don’t expect that we’ll find these names trading at a 10 point spread like 60% vs 70%.

They won’t be trading 60% and 120% to keep the ratio constant either. But there will be less error in assuming that then vega-weighting as if the spread will stay constant.

Once a grenade goes off, path dependence is likely to swamp much of the error around the edges as you will see your vegas grow and shrink as the spot moves closer or further from your strikes as realized vol starts interacting with the implied vols.

Neither weighting is a panacea for “Am I fully hedged?”

You should look at the history of a relationship to see if the ratio or spread appears to govern the bungee cord between the 2 names but my default is theta-weighting which implies more trust in the ratio.

Just remember:

  • if you are betting on the ratio, use theta-weighting
  • if you are betting on the spread, use vega-weighting

The vega of ATM options

Holding DTE constant, we saw that gamma and theta depend on the vol level.

You may also have noticed that vega didn’t.

The 15%, 30%, and 60% vol options all had about the same vega. That reality is why we used an equal weight for the legs of the trade when we vega-weighted.

So what does vega depend on?

This is neat — ATM vega depends only on the spot price and DTE. We are holding DTE constant.

[Note: When I use ATM here I’m technically referring to ATF or at-the-forward but I’ll just say ATM which is more familiar to most]

So ATM vega only depends on the spot price. If you double the spot price you double the vega.

The proof of this can be seen easily from the approximation of the ATF straddle:

If I re-write that, it’s clear:

Straddle = σ x (.8 * S * √t)

Remember vega is change in option price per 1 point change in volatility.

A 1 point increase in σ changes the straddle by .8 * S * √t

Ignoring time ‘til expiry, the ATM vega is strictly a function of spot price!

If we vega-weight a pairs trade and Stock A is half the price of Stock B you will need to buy 2x as many options on A. In the examples we did above, both stocks were the same price.

Final recap

Holding DTE constant:

  • ATM vega depend only on spot price. Even if a pair has different vols, to vega weight a pairs trade simply weight by the ratio of the prices. This is a bet on the vol spread.
  • Thetas are proportional to vol levels. To theta weight a trade, weight by the ratio of the vols. This is a bet on vol ratio.

Learn more

“Renting A Straddle”

This week, moontower.ai announced several free option calculators with more to follow.

💡These are embeddable so you can add them to your own websites, Notion workspaces, or wherever you organize your insanity.

One calculator that many of you might find useful is the Event Volatility Extractor.

If a known event such as as a stock’s earnings date announcement we expect the market to assign extra volatility to any expirations which include that event.

Option traders will decompose such an implied volatility into:

  1. A single day event vol or expected move size
  2. The typical vol or move size for a regular day

If you were looking at a student’s grade in chemistry you know it was the average of the tests. But if the final exam has a bulk of the weight and the remaining tests were equally weighted you have no way of backing out with the final’s weight was.

The option’s trader faces a similar problem. How much of the implied volatility is coming from the market’s estimate of the event move size?

The best a trader can do is tinker with assumptions for the earnings or event move and then see what that implies for a typical trading day.

An “expected move size” corresponds to the value of a straddle. By converting straddles into an implied volatility for that single day, we can back out the volatility that is equally assigned to the remaining trading days until expiry.

The larger estimated event move, the lower the implied vol must be for the remaining days and vice versa.

Application: “Renting” The Straddle

Imagine a 30 day option on XYZ stock. XYZ is announcing earnings the morning of the option expiry date and you expect that the earnings move will be 4%*. Therefore you expect the straddle to be worth 4% right before earnings are announced or about 80% volatility (see straddle approximation calculator)

But what if it’s worth 4% today?

  • A 4% straddle with 30 days until expiry corresponds to an implied volatility of 17.5%
  • We expect the straddle to be worth 4% of the stock price just before the last trading day. A 4% straddle corresponds to an 80% volatility with 1 DTE
  • Therefore, the implied volatility must increase from 17.5% to 80% between now and expiration. This increase in implied volatility will exactly offset the theoretical option theta if the straddle has remained a constant 4% of the stock price over the course of the month!
  • If a trader knew this, they could buy the straddle today, hedge the gamma and then sell the straddle before earnings is announced. This kind of trade is known as “renting the straddle”.

This example is idealized. The trader got to “rent a straddle” implying zero volatility for all the days preceding earnings. It was free gamma. The example is meant to illustrate the idea that implied volatility is not distributed evenly across all days and by “extracting” volatility ascribed to events you can make better comparisons cross-asset.

*Perhaps by looking at how the name has moved on prior earnings dates. Estimating move sizes is an active area of research for practitioners. You can think of the problem inversely – you can try to fit the event size to your estimate of a fair trading day volatility. It is common to use this calculator in both directions.

When Car Leases Offer Options For Less Than Zero

Car leases are said to be “an option to buy”. Put-call parity is the most important concept to understand about financial options. At the core it really means a call or put can be turned into a straddle. An “option to buy” or call is also an option to sell.

I’ve talked about this a couple times in the past, most recently in Car Straddles. We usually lease our cars. We’ve bought some out and other times we’ve put the car back to the dealer after the lease term. If you are certain you want to own the car for long time, you should just buy it. You typically pay a premium for the option. It’s explained in that other post and in a prior one, Are Car Leases Confusing?.

We won nicely on our last Highlander lease we exercised the option to buy when used car prices were nuclear in early 2022. The used ones were trading higher than the new ones because the new ones were scarce/back-ordered. We exercised the option by trading the old one at a much higher price than the residual back to the dealer for the single Highlander on the lot. It happened to be the spec we wanted and the same boring ass white as our old one. This is called being lucky to have poor taste.

The questionable taste continues today. It looks like we are going to pick up a Hyundai IONIQ 6. I bring this up because the lease pricing is especially interesting for the next 2 weeks. My BIL, knowing we were interested in getting an EV, sent me this Slickdeals promotion:

This probably explains why I’ve been seeing a bunch of IONIQ 6’s on the road very recently in my area.

We did a family test drive of both the IONIQ 5 and 6 yesterday. It was high-fives all around — the wife and kids approved. Way more fun than the Highlander.

But let’s talk money.

The promotion is indeed real. The dealers are doing $10,000 rebate promotions. $7,500 comes from the EV tax credit — I thought there were income limitations on these yet the dealer claims there isn’t a limitation. He didn’t strike me as a reliable witness but regardless there’s actually a loophole where they are allowed to pass them on through on leases.

Being my tedious self, I needed to go home and play with spreadsheets. I wanted to compare how much it would cost to buy the car in cash (assuming an outright purchase is still entitled to the $10k rebate that occurs up front) vs leasing the car then buying it out for the residual in 3 years. My presumption is the lease method would lead to an overall higher cost because the option has value and I’ve seen this to be the case before.

Here’s what I compared:

  1. Purchase

    This is straightforward…how much would it cost to buy the vehicle in cash including the 9.25% sales tax plus the scroll of fees.

  2. Lease

    The cost:

    full amount due at signing (down payment and bunch of fees)

    +

    the sum of payments over 36 months discounted to present value

    +

    the residual (including tax) discounted to present value

    I used an after-tax required return of 3% for the discounting. This is a conservative estimate. The higher the number you choose the more valuable the lease option and I’m trying to evaluate the lease conservatively.

Here’s the output:

Bizarre. Look at the “lease option premium” which I define as the lease-implied cost minus the cash cost.

You are effectively being paid to own the option. And if you can earn more than 3% after-tax on the cash you don’t spend up front, the lease is even better!

Unfortunately, I wasn’t able to check the pricing for other vehicles to see if this was just a Hyundai thing. The reason I couldn’t complete the exercise is it’s very difficult to find the “residual” amount in dealer lease quotes online. Without the residual, you can’t evaluate whether the lease payments are a good or bad value.

The online quotes are not thorough and more concerned with coaxing you into giving them your contact info rather than creating firm asking prices. I checked the websites for at least 15 car dealers in the Bay Area and the only ones that provided lease quotes with residuals were Toyota Walnut Creek and Hyundai of Dublin. Toyota leases were also more attractive than buying but Toyota is historically aggressive on lease pricing so it wasn’t extra informative.

Anyway, if you’re car shopping, I noticed there were a few brands in addition to Hyundai with steep discounts until June 3rd as extended Memorial Day sales.

Using Options Better

While a successful volatility trader’s edge is in discerning relative value between options, they are agnostic on the direction of the underlying. This is a niche symbiosis in the ecosystem of markets. The Egyptian plover that cleans the gluttonous gator’s teeth.

The wider, active marketplace, with deeper pools of alpha, sets the price of underlying assets. Fundamental and macro traders have opinion on direction but are agnostic about the price of the options. Just as the vol trader assumes the underlying is “fair”, the directional trader assumes the options are “fair”.

(moontower.ai achievement is bringing a vol trader’s discernment about the relative value of options to the directional trader)

So it doesn’t surprise me that most option users just think of calls and puts as levered directional bets. But an option’s contract is a bundle that prices financing costs, volatility and time. To think of them as firstly as directional tools is to not fully internalize how deep an insight the put-call parity identity is.

The price of an option is primarily about volatility.

[Just look at the decomposition of their p/l equation in A Visual Primer For Understanding Options]

Trading the stock is blunt 2-D expression of a trade. Whether trading the stock directly or an option to express a thesis depends on 2 prerequisites:

  1. The investor’s perception of the stock’s distribution over some period of time.

    This is embedded in any decision to click “buy” or “sell”. How explicit any investor’s targets are and what rules they keep for changing their minds spans the gamut from “vibes” to code.

  2. How that perception differs from the option market

To satisfy #2, you need to be able to interpret the what a vol surface is saying.

  • What does the straddle price mean?
  • What does a high or low skew mean?
  • How do I know if the skew is high or low?
  • What does the vol differential between months mean?
  • There are so many expiries and strikes, how do I discern which actions on which contracts at what size is the best expression of #1?

Or is the option surface saying that my view is “consensus”? In which case, the only reason to use the options is to sculpt your payoff profile for various scenarios. This exercise makes the trade-offs easily apparent.

[This sounds like a lot but on almost a daily basis I step people through questions like this in the time it takes to have coffee. Half the battle is the options are a second-language problem — and I don’t mean in the jargony sense — I mean it in the I-already-know-the-words-but-I-still-translate-them-instead-of-thinking-in-option-language-natively.

Which is probably why I have a habit of explaining option ideas with my hands automatically. Option sign-language is hockey sticks paths through time embodied.]

Over the years of talking to non-vol traders I have found that option users fall in 2 categories:

  1. Levered directional players who do not understand that options price volatility and distributions (This discovery peaked during WSB/Reddit heyday and inspired How Options Confuse Directional Traders)
  2. Investors with an intuitive understanding of options as distributional bets

My grand treatise for group #1 is: Celibacy Vs Condoms: The Answer To Whether You Should Trade Options

For group #2, sit up tall!

You don’t need to have a view that sounds like “this option is priced at 24% vol and I think vol is going to realize 28%”. It’s enough to understand:

  • “I’m buying this call because if the stock is up 10% it’s up 20%” (conditional probability of discontinuity)
  • The distribution is more bimodal than the option’s market seems to think. One of my favorite examples of this was in The Big Short when the Cornwall guys bought far OTM calls on Capital One because they understood that when the bank was cleared by regulators the stock would be much higher. These were not option guys, but they recognized that the option’s prices didn’t agree with their expected value in what was a discontinuous scenario.

Practical tips

The following ideas are shareable parts of conversations I had with a family office that uses options.

 

On Risk Budgeting

I was chatting with a family office that uses options (outrights or vertical spreads only) on less than 10% of their trades. They are not vol traders but will use options for 2 reasons:

  1. “Cornwall” reasoning — they believe the options are mispricing the distribution
  2. They have a directional view but don’t want to be shaken out of the position due to path.

I’ve addressed #1 above as a great use-case for options. I remind everyone that options are priced for specificity — if you have a variant view of the market, an option is a highly levered exposure to your thesis being exactly right. (Which is why options are the weapon of choice for crooks trading on MNPI. And also why the SEC monitors unusual behavior in single stock options closely.)

#2 is another fitting use for options. I call it managing destination vs path. A small percentage of my trades also fit this pattern. A low delta call that you think is 4-1 to go ITM but if it does you expect it will pay 10 to 1.

This style of trade is called risk budgeting because you decide how much you are willing to lose in advance. “I’m willing to incinerate $1mm on these calls”. When I did such trades, I segregated the risk in an alternate view or what I called the “back book” (careful in the world of pod shops this term means something different — but I was calling it that 15 years when I was on the floor).

You segregate the risk because you don’t want to hedge the gamma or greeks that the option spits off. You’re betting on terminal value not path. If you hedge the gamma you are changing the payoff profile and can now lose more than your initial outlay. [If a stock grinds up to your long strike and expires you will lose the option premium. If you sell shares to hedge the delta the whole way up you lose on all those trades as well].


I asked these investors if they ever roll the OTM calls down if the stock falls? In other words is the terminal value target related to moneyness or absolute price.

What governs their rolling rules?

The answer was basically “feels”.

And I take no issue with that. I’m the last person who is going to condemn a trader for bringing the ineffable interpretation (I prefer “unstructured data”) of various moves into their decision process.

[Discretionary trading has an irreducible amount of “finger in the air”. Will some dolts lean on that as cover for their impulsiveness? Sure. What can I tell you — ambiguity is hard. But over enough reps, your judgement of a trader on a mix of performance and how they narrate their thought process is on more solid footing than your judgement of your primary care physician. Have a sense of proportion.]

The actual they gave was “well, if the stock goes down after we bought the calls we just accept that we were probably wrong and let it go”.

That was a bit head-scratching for me. Like the probability of the stock closing at a price at some point below the price it was when you bought the call is close to 100% (you could re-phrase this as “what’s delta of an at-the-money one-touch put?”).

The answer was a bit too low-res and self-defeating imo. After all, the majority of a stock’s move is systematic risk not “idio”. So the logic just collapses to “if the stock market downticks, we are wrong about this stock”.

I proposed:

What if you normalized the stock’s move by its beta and a confidence interval? So if the stock market is down, but your name is down by much less, than you were actually right on the name. How about test all those cases to see if a rule like

  • If market is lower, but stock outperforms then re-strike the option (ie roll the calls down)

There are still messy details like “how often” but this is an example of a wider lesson that I harp on — measurement not prediction. By measuring in absolute terms, you get one answer — “we are wrong”, but in relative terms you could be right. But the logical leap in how to measure comes from understanding reality clearly — every stock move is mostly systematic. It’s part of a basket that by index arbitrage imposes flows in the name based on what the index futures do.

Another thought

There’s an asymmetry to rolling. If you buy a 15 delta put and the stock rallies, vol likely declines. Even if the put skew increases, there’s a good chance that rolling the puts up will feel like a bargain compared to the opposite scenario — where you bought a 15 delta call, the stock falls, vol expands and the call spread you buy to roll down feels rich.

Rolling puts up feels better than rolling calls down.

I come from a tradition that needs to measure everything in pennies. So I might be splitting hairs to a fundamental investor. But it did remind me share something I like to do:

Throw everything in a scatterplot!

What’s the price of a 30d delta/10 delta call spread as a percentage of the spot price for various vol levels. This nets out the impact of ATM vol changing while the skew changes. Vol is lower but the put skew is higher. Ughh, just show me how much premium as a percent of spot that spread costs.

More scatterplot tips

1) Restrict ranges to consider conditional probabilities.

If you fit a regression line between vol level and put skew you will see that skew flattens as vol increases. If you restrict your sample to a regime (say to when SPX vol is sub 10%) that line will be steeper. If you were looking to buy puts, every time vol was cheap, you might be deterred because skew was in the 75th percentile. But maybe that same skew is in the 40th percentile conditional on ATM vol being below 10%?
[I will pull the data and show this picture in another post but I’m writing this off the cuff]

2) Color code the dots to show time

IYR realized vol has been falling and since the VRP ratio has been stable that means a short vol position has the wind at its back as both the IV and RV are declining.

via moontower.ai

You can hack your way to a lot of intuition by throwing data on scatterplots and jamming a line through it.


If you use options to hedge or invest, check out the moontower.ai option trading analytics platform

Mermaids, Fireflies, and the Bid-Ask Spread

A reader asks:

Do you have any insight into the activities of market makers when they act as authorized participants in the ETF market?

If you ask the internet how market makers earn profits, the typical response is something like “by capturing the (bid-ask) spread.” I have always wondered how “capturing the (bid-ask) spread” can be so enormously profitable and consistent.

I have been looking at deviations of ETF prices from net asset value and am now under the impression that “spread” means something totally different to the market maker (in particular, authorized participants).

Am I way off here?

 

My answer below, plus some story-telling on ETF options and option market-making generally:

ETF market-maker life

I was an ETF market maker for SIG for a bit and we were APs.

It makes more sense when you remember that liquid names in anything don’t really need market makers because there’s enough organic liquidity.

[Aside: This is a broadly useful insight — it’s an important part of the meta of when and where to shift gears back-and-forth between position trading and bookmaking]

To answer the question:

  1. there is a very long tail of ETFs that might have plenty of edge in them but just don’t trade lots of volume.
  2. the cost to create/redeem is very low and large mm’s have economies of scale (good funding rates, low commissions, fast execution) so they can make money with 1/2 cent of edge on a trade.
  3. published intra-day NAVs are often wrong especially when you get into more complex ETFs (the spreadsheet to price HYG or FEZ is a giant book with many assumptions because there’s a staleness in the prices of the underlying components — so you need a model for guessing what the fair current price of the components are — think of a European ADR price after the local market has closed but the US is still open — you might “beta” the stock to the SPX from when the local market closed while adjusting for the currency-cross tick by tick)

There are several firms that have built large businesses on the back of trading ETFs across time zones and internationally as the markets open from Asia to the US. Billions of dollars have probably been made on this in the past 2 decades. [Redacted list] of under the radar places all made this their bread and butter. In fact, they were way more focused on this than options.

US equities were super competitive back in 2004-2005 when I was doing this — and that’s even after adjusting for SPX futs prem/discount.

To explain that more clearly:

  1. we’d compute the current price of SP500 basket using direct data from the exchange feeds
  2. add the fair value of the EFP (cash-futures swap) to create the fair value of the synthetic future
  3. then compute the premium-discount by subtracting this synthetic from the actual SP500 futures price. If that number was positive we’d say the futures were trading “over” by say 10 bps or whatever that premium represented.
  4. we’d then beta weight the ETFs by that premium to predict the true fair value of the NAV (basically this all comes down to the fact that futures lead the cash)

This was standard practice 20 years ago if not more.

A few more tedious details:

  1. We were computing NAVs based on the files sent to us by the actual ETF sponsors every morning including how much cash on hand the (this was called a “cash plug” in our lingo) sponsor had in the ETF portfolio based on the prior day’s create/redeem activity.
  2. Computing the fair value also requires knowing the true borrow rate for every name because that is an input (although that can sort of be aggregated from knowing the EFP market since it should be incorporated into the cash/futs arb).

The general tradeoff you’ll face

More liquid names will have no edge but you can execute.

Less liquid names might have flow-driven mispricings that market makers are not closing (because they might know a premium is going to become more premium for example) but execution is harder.

Also, there’s massive adverse selection in this — if you are getting filled easily there’s a problem. When you get into the nitty-gritty of ETF arbitrage you are in the realm of understanding the prospectus — market makers trying to pick off other market makers based on some small legal gotcha or upcoming reconstitution of an index (I’m vague on the details but I remember the Holders ie TTH, SMH going thru some change that a few market makers recognized before the rest and picked them off by dumping long dated option premium on them that was about to evaporate. That one might have ended up in court.)


Shifting to options now…

Here’s one to ponder:

Option quotes are streamed in accordance to where a market maker thinks they can get their hedge off in the underlying. Typically the options will be priced off the mid of the stock’s bid-ask.

But if a market-maker is quoting ETF options and believe the NAV is different than the midpoint what does that mean if the option customer gets filled?

Option market maker life

Capturing the bid-ask is more cloak-and-dagger than the simple spreads you see on the screen. A professional market maker can see the screens, but their job is constantly update “what’s the true bid and true ask?”

A friend who was the lead mm in a semi-liquid options market used to describe his job as “throwing dust in the air so nobody sees where it really is”.

An options market with sparse or wide screens might trade way tighter via voice (especially in ETF options). The screens can be framed however in anticipation of an order or to entice someone to buy or sell.

Trying to figure out fair value in a name that trades by appointment is like trying to catch fireflies that blink every so often. The 3-month 25d put just traded near the offer…is vol higher or is put skew higher? If the straddle was offered by another party at the same time then the skew is probably just higher now. Maybe the straddle seller is making a statement about vol since they are, well, trading a straddle but the put buyer is betting on direction. In that case, maybe I pass on the straddles, sell the puts and hedge their delta and wait for the straddle seller to step down even cheaper. Then I’m synthetically legging ATM/25d put spread for a cheap price. Sizzler’s on me tonight.

But what are the chances the straddle seller is going to step down and lower the price? Have I seen the signature of this order before? Can that help me handicap their tendency?

What about the put buyer…do I think I’ve seen them before?* Do they tend to be smart on direction? In that case I want to hedge the put sale on a “heavy” delta.

All of a sudden a call buyer shows up in a deferred month. Do I think the term structure is shifting? Which one of these orders is the most aggressive?

If this sounds like fun it actually is. You are playing Sherlock Holmes in real-time with quick feedback. Especially if there’s so much action that there is 2-way flow simultaneously. If any of you came to the mock-trading sessions we did for StockSlam/Pitbulls you know the feeling of needing to hold a bunch of info in your head at the same time, maintain your ability to listen, and quickly react before the right trade is obvious to everyone else. Which is why experience and feel are crucial — you need to maximize the ratio of “good decision” to “how much info I need”.

Slow and stupid are indistinguishable in the market-making game. It’s not good enough to be “faster than average” in a winner-take-all ecosystem.

*People wonder how you can know “who” it is. You can’t know for sure, but you are pattern-matching. Have I seen an order of similar size, aggressiveness, time of month, moneyness, thru this particular broker, and so on. And if you roll, you’ve shown me the Monty Hall donkey.

Look, if you’re an account trading options in the voice market you are probably a repeat player. Maybe you have a periodic hedging program. Maybe you keep coming back because you’re winning. Oh, I remember trading against Mr. “This-Is-The-End-Of-The-Order”.

And brokers themselves have niches. When I hear a French accent I already know what class of customer is on the other side of the phone.

“Allo, dis is ah bee-yair”

Hi Pierre. I assume you will be joining the screen bid?

“ah-ah, yoo noh meh too well”

I’m going to level with you mon frere. It’s a rev/con. I’ll still be bid there myself next Monday.

“vat ah-boot for hahf koh-mee-see-on”

See, Pierre, the Royal Pierre who stands in for the French national pastime of clinically computing hedge ratios to 14 decimal places, is more price sensitive than extreme couponers because his client is protecting the margin on a structured note sold to private wealth account and the sales team get 99% of the p/l attribution, while the exo trader shakes a tin can on Wall Street for someone to pair off risk at fair.

Now the regional broker based out of Florida — he I’ll pay double comms to fund his cargo-short wearing client’s appreciation of Mermaid’s dancers.

So sure, the market maker doesn’t know the client’s blood type. But it’s hard to fool people twice.

Life Settlement Arbitrage

A guest post showing how “markets find a way”

My friend Rajiv Rebello has helped both my family and extended family navigate the complexity of insurance contracts. That world is coated simultaneously in both exploitive grease and heavy regulation. Rajiv is our white knight. Brilliant, honest, and experienced. He’s an actuary who help individuals find policies and understand the opaque pricing and incentives. He has helped buy-side firms price policies as investments.

He was instrumental in my research when I investigated and published Using Insurance For Tax-Free Investment Growth.

A few days ago I sent him Matt Levine’s article Apollo Had Some Death Bets.

“Rajiv, pretty please explain what the hell is going on here in more detail for Moontower readers”.

He hits it out of the park.

He breaks down the incentives, arbitrages, pricing and chicanery in the life-settlement primary and secondary markets. And you will learn plenty about insurance that is directly actionable and applies to your own policies!

Before we start, give his Substack a follow (especially since I selfishly asked him to start one): Separating Value From Bias


Life Settlements: A prime example of markets finding a way—albeit in an unbelievably messy fashion

When it comes to financial decisions, humans tend to behave in ways that are suboptimal and not in their best interests—and entire industries are made to profit off this. The only thing that holds them accountable is another industry trying to make a profit off the first.

When the first Jurassic Park movie came out in the summer of 1993, I, along with the rest of the country was blown away.

I was only 12 years old, but had never seen anything like it.

For god sakes, they brought dinosaurs to life.

If you haven’t seen the movie, here’s a quick synopsis: A couple of paleontologists visit a secret animal park that’s managed to clone dinosaurs and bring them back to life. They’re supposed to go on a straightforward tour of the park and give their approval so that they can open the park to the public.

It’s supposed to be a very controlled experience with numerous safety protocols and checks and balances to prevent anything from going outside of what was planned.

There’s a line in the movie that summarizes the gist of it well. One of the scientists of the park is trying to explain how the dinosaurs in the park can’t reproduce because they were genetically engineered to all be female.

To which, Jeff Goldblum’s character—whose primary role in the movie is to point out the human folly in trying to suppress the insuppressible—says:

“If it’s one thing the history of evolution has taught us is that life will not be contained, life breaks free, it expands to new territories and it crashes through barriers, painfully, maybe even dangerously, but……

…life finds a way”

And as we’d later find out, all hell breaks loose, life finds a way, and the best laid plans of mice and men oft go awry.

I can replace that same Jeff Goldblum quote except by replacing “life” with “markets” that perfectly encapsulates the life settlement industry.

“Markets will not be contained, markets break free, they expand to new territories and they crash through barriers, painfully, maybe even dangerously, but…..markets find a way”.

Since Moontower often takes deep dives into how opposing counterparties of a trade value an asset and the psychologies involved, I thought it might be worthwhile for readers to explore the life settlement industry from the position of a counterparty trying to even out an asymmetric imbalance of power and control between the life insurance industry and the consumer.

Ultimately the life settlement industry is forcing the life insurance market to be less predatory with its own consumers—it’s just that the life settlement industry is using the same exploitative tactics that the insurance industry is in the first place.

Matt Levine/Life Settlement Summary
Matt Levine’s article centers around the story of a $5 million life insurance policy that was sold to a woman in her 70s.

While this sounds like a non-descript transaction, the unique element of the story is that an investment entity—unrelated to the elderly woman (i.e. the insured)—paid for the premiums on the policy on condition that the investment entity would receive the death benefit when she passes.

On top of that, the investment entity paid the insured a $150,000 bonus as an incentive to apply for the policy all so the investment entity could have the obligation of paying all the premiums on the policy and the right to receive the death benefit when she passed away.

A blue rectangle with white textDescription automatically generated
In a life settlement transaction an investment entity pays the insured on a life insurance policy an upfront price in exchange for ownership interest in the policy. The investment entity then pays all premiums on the policy going forward and receives the death benefit when the insured passes away.

You might be wondering why an investment entity would do this.

The transaction, when done properly and legally (i.e. not what was done in this case) is called a life settlement.

life settlement is when an existing policyowner of a life insurance policy sells his or her interest in the policy to a third party for an amount larger than he or she could get if the policy were just canceled.

This particular transaction wasn’t a legal transaction because the investor can’t entice the policyowner to buy the policy in the first place. Doing so violates the insurable interest provision required of a life insurance policy since an outside investor who doesn’t know the insured doesn’t have a vested interest in the insured staying alive.

The investor can only legally acquire the policy after the insured purchased the policy on his or her own without influence from the investor.

While the Levine article gives off the idea that there are a lot of illicit transactions happening in the life settlement space, the truth of the matter is that this policy was issued back in the mid-2000s when there was a lot less regulation of the space than there is today.

Today this transaction would have been most likely caught in the due diligence phase of the life settlement process and wouldn’t have proceeded.

The reason why the investors in this case enticed the policyowner to buy the policy and sell it to them in violation of the law was because they saw a huge arbitrage to be made between the cost of acquiring the policy (premiums to the insurance company and payout to the insured) and the value of the death benefit.

The investors believed they had an upper hand over the insurance company that was worth them violating the law.

Levine quotes this as being a pure mortality bet, that’s not the full story.

Remember that the insured was applying for a life insurance policy. Which means she would have had to get a medical exam and all her medical records would had to have been sent to the insurance company.

So it wasn’t a pure mortality arbitrage here. The insurance company had the same medical information as the investment entity.

The arbitrage came from the fact that the cost of the insurance policy relative to the health of the insured was low and the investment entity planned to pay premiums on the policy in a manner that exploited this.

The investment entity was exploiting the pricing design of the life insurance policy as opposed to just a bet on the mortality of the insured.

Which should bring up an interesting question for you as a reader.

Why would an insurance company ever design a policy in which the cost of insurance they were charging was lower than the underlying mortality cost of the insured?

The answer is that they expected that the policyowner would behave in ways that would reduce their risk of having to actually provide that insurance.

Pricing of a Life Insurance Policy

In order to understand why an insurance company would charge a cost of insurance that was less than the cost of mortality, you need to understand how a life insurance policy is designed.

We all know that the chance of someone dying increases as they get older.

If you were to design a life insurance policy the natural assumption would be to charge a cost of insurance that was higher than the cost of mortality for every year that the insured was alive.

So for example, if there was a $1M policy and there was a 1% chance of the person dying in the first year, that means you would expect a $10,000 loss due to that policy. So if you wanted a 10% profit margin on your risk you would charge $11,000. That would give you a $1,000 profit.

Analogously, in the second year if there is a 2% chance of the person dying, to keep that 10% profit margin you would charge $22,000. Now you have a $2,000 profit in the second year.

If you were to price a life insurance policy like that the economics would look something like this:

Normal Profit Margins of a Company

A graph of cost of insuranceDescription automatically generated
A normal profit structure is to charge a cost of insurance to the customer that is a fixed percentage over the underlying mortality cost of providing that insurance.

We can notice a couple of things here.

  • While the profit margin is always 10% greater than the cost of mortality, the absolute value of the profits increase over time because the underlying cost of mortality increases over time.So the bulk of the profits come in the later years.
  • Equivalently, the insurance company could price the product such that they take larger profits in the earlier years and then losses in the later years.

Unequal Profit Structure

A graph of cost reductionDescription automatically generated with medium confidence
An unequal profit structure charges a cost of insurance (orange line) that is significantly higher than the underlying cost of mortality (blue line) in the early years and a cost of insurance that is lower than true cost of mortality in the later years

While the chart isn’t exactly drawn to scale, you might notice that the losses in the later years are larger than the profits in the early years. However, remember that the net present value of those later year losses are smaller than the profits in the early years.

In both pricing examples, the net present value of the profits are the same as the earlier chart which charged a cost of insurance that was always a multiple of the true cost of mortality. So the insurance company would, in theory, be indifferent.

While the second pricing design introduces a future liability, part of the large profits in the early years would be used as a reserve to meet those future liabilities.

Premium and Lapse Supported Pricing

However, it’s important to note that policyowners typically behave in ways that significantly reduce the cost for the insurance company to provide the insurance:

They pay more for the mortality cost in the early years of the policy and less than the mortality cost of the policy in the later years

Most of you reading this probably have a term life insurance policy to protect your spouse and kids. Maybe you got a 20 year term or 30 year term policy. However, even though the chance of you dying increases as you get older the premium you pay every year is the same regardless if you are in year 1 or in year 30.

What this means is that you overpay the cost of the policy in the early years, and you underpay the cost of the policy in the later years.

Level Premium Payment vs Underlying Cost of Mortality

A diagram of a cost reductionDescription automatically generated with medium confidence
When you pay a level premium into a policy with increasing costs, you are essentially overpaying the cost of mortality in the early years and underpaying it in the later years

So the cost of you dying earlier in the term is partially offset by the fact that you also overpaid for the policy in the early years as well.

2) They cancel the policy before the term is over

If you buy a 30 year term policy, approximately 60% of you will cancel the policy before the 30 years are over and about 40% of you will cancel it within the first 10 years.

This further reduces the liability for the insurance company—especially when we consider the fact we mentioned above about policyholders paying more than the cost of the insurance in the early years of the policy.

It’s a win-win for the insurance company: you pay more than you should in the early years of the policy and then you cancel the policy before it ever gets to the part in the term in which you are underpaying it.

The insurance company collects excess premiums for the coverage they offered you.

This is why an insurance company can design a policy that has high profit margins in the early years and large liabilities in the later years. The insurance company expects the profits to materialize in the early years and the liabilities in the later years to never come due.

When insurance companies do this too aggressively, it’s called lapse-supported pricing. “Lapse” is insurance jargon for “cancel”.

While not all life insurance companies are this aggressive in their lapse-supported pricing, all life insurance policies are based on the design of a large number of policyholders paying a level premium — overpaying in the early years and then canceling before they can ever receive the benefit.

Policyholders are humans. And humans act on emotions which they use to justify their logic instead of the other way around.

Insurance companies know this.

Policyholder behavior reduces the cost of mortality for an insurance company. This increases the present value of the insurance companies’ profits and reserves and reduces their future liabilities.

Policyholder Behavior Reduces the Underlying Cost of Mortality of a Life Insurance Policy

A diagram of a line of a personDescription automatically generated with medium confidence
Policyholder behavior reduces the insurance companies’ underlying cost of mortality from the blue line to the green line. This increases the insurance company’s early year profits and reduces the future year liabilities for the insurance company.

It also reduces the cost of the insurance to the policyholders who keep the policy for the long-term at the expense of those who do not.

If everyone were to keep the policy and behave the way an optimal investor would, the cost of your life insurance policy would be 2.5-3 times higher than it currently is.

So if you have a life insurance policy and are actively paying the premium, you should thank the 60%-70% of people who pay more than they should and cancel it early for subsidizing your policy.

What the investors in the Matt Levine article did was identify life insurance companies that were using a high degree of lapse-supported pricing. They realized that if they purchased enough of these policies on elderly individuals and paid just the cost of insurance on the policy and nothing more, they could profit off of the design of the policy by acting in ways that the average policyowner wouldn’t.

It allowed these investors access to an investment in which the underlying cashflows were not correlated to equity markets. By acquiring multiple policies on multiple insureds, it allowed them to diversify their investment risk.

Exploiting the Insurance Company that is Exploiting its Customers

Back in the mid-2000s when the policy in the Levine case was sold, overly aggressive lapse-supported pricing in the life insurance space was a lot more prevalent than it is today.

If you think about it, it’s an almost perfect design.

The design reduces the cost of mortality for the insurance company. This means that the insurance company can reduce the premium it charges for the insurance product.

Which of course means it can sell more policies since it’s a cheaper product and capture a larger share of the market in comparison to its competitors that don’t use that design.

The problem comes about when sophisticated investors like the ones in the Levine article act in ways that maximize the value of the policy as an investment for themselves at the expense of the insurance company.

When investors do this, all of a sudden those large future liabilities that the insurance company never expected to come due are in fact poised to come due.

However, insurance companies have an out here which is protected by law.

Insurance companies are allowed to use future assumptions to price their life insurance products. If those future assumptions with regards to policyholder behavior prove to be inaccurate they can later say, “whoops, my bad” and increase the cost of insurance for all policyholders.

It’s another win-win for the insurance industry.

Price the product below the true cost of mortality to gain market share and collect early profits. If you end up being wrong later, just increase the cost of insurance across the board for all your policyowners who purchased a long-term contract from you and are now stuck with it.

If this seems deceptive and like a bait-and-switch, it more or less is.

Doing this not only damages the brand and reputation of the insurance company at hand and they expose themselves to large class action lawsuits.

Interestingly enough in these class action lawsuits the life insurance companies have actually acknowledged that the reason they had to increase their cost of insurance was that sophisticated investors purchased these policies and utilized them in ways that they didn’t anticipate.

This is indirectly saying that they expected their policyholders not to be sophisticated and NOT to act optimally.

The pricing design only works the way it’s expected if the insurance company is exploiting individual policyowner behavior and those policyowners are not en masse using the policy design of that said insurance company in a way that benefits the individual policyowner.

Which is, of course, where the life settlement industry comes into the fray.

Life Settlements: Exercising an Embedded Option
While life insurance companies can increase the cost of insurance across the board for policyowners based on aggregate policyholder behavior or mortality assumptions, they can’t do it on an individual level.

For example, if you are in great health when you buy a life insurance policy and then a couple of years later put on a lot of weight or have a serious health event, the life insurance company can’t raise the cost of insurance even though the chance of you dying has increased.

There is a mortality arbitrage between the cost of insurance of the policy and your underlying health.

The policy, as an investment, is worth more now than it was when you bought it.

However, the insurance company won’t compensate you for this additional value.

If you can’t afford or no longer want to pay the premiums on the policy you have limited recourse other than canceling the policy for a fraction of what it’s worth—which is of course what the life insurance company is expecting you to do.

This is where the life settlement industry steps in.

It understands there is value being lost here and helps bridge the gap between the low value the insurance company is offering you if you cancel versus the intrinsic value of the policy as an asset.

So when you buy a life insurance policy, you are also getting a free out-of-the money put option from the life settlement market—it’s just that the insurance company doesn’t want you to know about it.

That option only becomes in-the-money if you have a health event that changes your underlying cost of mortality, or the pricing design of the underlying insurance product can be exploited, or some combination of both.

If your only options are to cancel the policy or sell it on the life settlement market, you are undoubtedly better off exercising that option and selling it on the life settlement market.

That being said, you and your family are better off keeping the policy and paying the minimum cost of insurance until you pass away because of the economics involved than selling it in the life settlement market.

In the case example we discussed above, the insured was paid $150,000 upfront so that the investors could pay the premiums and receive the death benefit when she died.

However, if the insured would have not taken the upfront offer, and knew to pay only the cost of insurance and not more, she could have paid the premiums and received the $5M death beath benefit tax-free. Her tax-free IRR on the transaction would have probably been close to 20%.

It’s hard to beat that elsewhere.

Instead the insured received a fraction of that value so that the life settlement investment entity on the opposite side could take the longevity risk and receive the bulk of the rewards.

Life Insurance Industry vs Life Settlement: Choosing between the Velociraptor and the T-Rex

In the climactic scene of Jurassic Park at the end of the movie, the velociraptors trap the paleontologist and 2 kids in a museum and are about to pounce and eat all of them when the T-rex busts in the door and starts attacking the raptors allowing the paleontologist and the kids to escape.

A cartoon of a person with two dinosaursDescription automatically generated
Life Insurance vs Life Settlement Company: Trapped Between Two Predators The life insurance company and the life settlement company create an environment that makes it easier for the policy owner to escape. But you don’t want to be trapped in a room alone with either of them.

That’s how I look at the battle between the life insurance industry and the life settlement space.

The life insurance industry is like the raptors.

The whole movie they have created an elaborate trap for you to walk into without you realizing that you’re walking into it.

Because that’s what people do—we walk into traps.

The only thing that ruins their trap is another brutal goliath also looking to devour you.

The life settlement industry doesn’t have your best interests at heart either.

When you sell a policy your the life settlement market you pay 15% to 30% in commissions just to give an investor the opportunity to purchase your policy and make a 15% to 20% IRR that you could have been making if you kept the policy.

They are the T-rex in the scenario.

Being trapped between the two isn’t the ideal situation to find yourself in.

But much like the protagonists in Jurassic Park, it’s the fact that the one monolith opposes the other that gives you the chance to walk away without being completely eaten alive.

On Markets Always Finding A Way

And that’s why markets always find a way.

One party can lay a trap for an innocent passerby, but as soon as another party realizes that they can eat off that same trap too, they’ll find a way to disrupt the first party’s business model.

It’s why Dennis in Jurassic Park turned off all the safety systems and tried to escape with dinosaur embryos so he could sell it to someone else.

The reason why the life settlement industry is messy and inefficient as opposed to other disruptive industries is simply because it can afford to be.

It’s not like other industries where you have to struggle to add additional value just to compete.

There’s plenty of profit to be skimmed off the consumer without them understanding the value that’s being lost.

The consumer is ill-informed and buying off emotion rather than logic or value.

That’s what led them to be stuck in the trap in the first place.

But Jurassic Park only works the way it’s supposed to if the animals in the park behave the way they’re expected to.

As soon as they start to test the boundaries and limitations of the fence it built to contain them, it has a problem.

If the average consumer understood the trap being laid for them, they would have exploited it for themselves instead of needing the life settlement industry to help them do it—all while the life settlement industry keeps the bulk of the economic benefits for itself.

The consumer is just a pawn being played in the middle of a trap they don’t know they are in.

They lose on the front-end when they buy a life insurance policy they don’t fully understand how to utilize in their best-interests.

And then they lose on the back-end when they sell an asset on the life settlement market for a fraction of what it’s worth.

The calamitous effects on the end consumer in the life insurance and life settlement industries highlight some of the most problematic elements of capital markets that invariably bring up questions of fairness and equality.

Is it fair that a large majority of policyowners overpay for a product so that a few can get the benefit?

Or that the majority of those getting the worse end of the deal are from lower income brackets so that those in higher income brackets can get the benefit?

You might say no.

But then if I ask you if you want to pay 2.5-3 times more for your life insurance policy you’d also say no.

But you can’t have one without the other.

Is it fair that if a policyowner can no longer afford or no longer needs their life insurance policy their best option is to sell it on the life settlement market for only a fraction of what it’s worth?

Again, you might say no.

But if it wasn’t for the life settlement market you’d cancel the policy to avoid the obligations of future premium payments that you can’t afford or don’t want to pay and receive a much lower payout from the insurance company than what the life settlement industry is willing to provide.

So what’s the answer here?

The answer is for more people to understand the mispriced opportunities in the life insurance market and exploit them in the same way and start making better decisions.

And the opportunities here are endless because they’re all designed around poor policyowner behavior and consumers making bad decisions.

It’s not like traditional capital markets where in order to get an advantage you have to be smarter than the trader on the opposite side of the table who has a PhD in statistics and decades of experience.

In this case, you just have to make better decisions than the average consumer.

So if you and a friend are being chased by the velociraptor that is the insurance industry and trying to gain an advantage, you don’t have to be faster than the raptor to do it.

You just have to make better decisions than your friend.

And your friend is making poor decisions based on emotional biases over a product he or she doesn’t understand.

It’s not rocket science, but does require intention, discipline, the willingness to learn and admit your flaws, and find people with the right expertise and intentions to assist you.

Exploiting these loopholes forces the industry to adapt.

Aggressive lapse-supported life insurance products are no longer as prevalent in the life insurance space as they were in the mid-2000s in part because the industry got burned heavily from life settlement investors exploiting this design.

Competition is what forces industries to deliver higher value to its consumer.

In the absence of this competition—and a misinformed consumer base—there is no incentive for the life insurance industry to change.

It’s easier for the life insurance industry (and many other industries) to just sell its consumers a story based on a false expectations and have them fall into the trap it designed for them.


About the Author
Rajiv Rebello is the Principal and Chief Actuary of Colva Insurance Services. He helps HNW clients implement better after-tax, risk-adjusted wealth and estate solutions through the use of life insurance and annuity vehicles.

He also writes a Substack called Separating Value From Bias where he explores inefficiencies in the financial and insurance space and how to utilize financial planning tools more effectively while connecting these issues to broader capital and social systems.

He can be reached at rajiv.rebello@colvaservices.com